Such people are terribly ignorant at best, and outright liars at worst. Invariably their founding tenet is that they are the sole custodians and guardians of "the pattern" of worship found in the New Testament.
Therein rests the fallacy of their argument. One that betrays as much a lack of faith in God as it does an ignoble grasp of theology.
Because to claim to be the "one true church" or the "restored church" or whatever is to imply, nay confess before all that Christ's Church is so invirile, so impotent, so corruptible and so weak that it has not survived and prevailed for these two millenia!
So let me put it succinctly and with some bluntness: the New Testament age... never ended.
Oh sure, the New Testament writings came to an end, when John finished his manuscript in his cave on Patmos. The time of the apostles eventually drew to a close when John died.
But the New Testament era itself?
Nope. It's still here. We're living it even now.
Where is the church of the New Testament, then? I'd say: pretty much anywhere and everywhere. It's wherever it needs to be. It is what-ever it is required to be! It becomes... all things unto all men, so that Christ is preached.
Who are the New Testament Christians? Me and... well quite a lot of people, I can tell you that! And a lot of 'em, are some that many of us don't appreciate that they are seeking after and serving the Kingdom just as we are, albeit perhaps in different ways.
I've been thinking quite a bit lately about something that Billy Graham is famous for saying: "Go to the church of your choice." And he's right. Go and worship at the place where... well, wherever it is that you believe that God is leading you to worship Him at. It could be at a Methodist church. Could also be a Baptist church. Or a Presbyterian one. Or a Roman Catholic assembly. Or a Mennonite place. Or a Seventh-Day Adventist congregation. Or a Church of Christ. Or a Lutheran gathering. Or Pentecostal. Or... need I go through them all?
So long as it is a matter of sincere conscience between you and God, it does not matter where I or anyone else tells you to worship Him at. You aren't even obligated by any of us to attend regular worship services if that is how He is leading... but as the writer of Hebrews cautioned, there is a danger in complete forsaking of assembly.
The New Testament Church didn't go away. It's persisted and endured for nearly two thousand years. It is not a brittle thing ready to collapse at the first mild breeze, but a robust edifice built upon a firm foundation. And though I wouldn't dare ascribe any like import to my own writing on par with that of Jude or James, I can at least smile a little in the assurance that mine is a role not unlike Polycarp (in spirit if not in style). The church survived those early years in spite of the weaknesses of men like Peter and Paul, and it will endure in spite of this man's weaknesses also.
I am the New Testament Church... and so can you!